The total operating revenues of a public transportation authority are $100 milli

Question

The total operating revenues of a public transportation authority are $100 million while its total operating costs are $120 million. The price of a ride is $1 dollar and the price elasticity of demand for public transportation has been estimated to be -0.4. By law, the public transportation authority must take steps to eliminate its operating deficit. (a) what pricing policy should the transportation authority adopt? Why?

(b) What price per ride must the public transportation authority charge to eliminate the deficit if it cannot reduce costs?

Explanation / Answer

(a) Price elasticity is negative (-0.4). So, It means demand is inelastic. So, the % change in quantity demanded is smaller than that the % change in price. Hence, when the price is raised, the total revenue will increase. Thus, the public transport should increase the price of ride.

Answer 7(b) Total operating cost is $120 million.
since the transport authority cannot decrease the costs, it should increase the revenues to $120 million in order to eliminate deficit.

Price elasticity is -0.4. It means, 1% increase in price result in 0.4% decrease in demand.
Let the firm increases price by x%.
So, new price = 1 + x% of 1 = 1+x%
New demand = 100 - 0.4x% of 100 = 100(1-0.4x%)
So, revenue = price*demand = (1+x%)*(1-0.4x%)*100 million = 120 million
=>(1+0.01x)(1-0.004x) = 1.2
=>(1-0.004x + 0.01x -0.00004x^2) = 1.2
Since 0.00004x^2 is very small, we ignore it.
=>(1-0.004x + 0.01x) = 1.2
=> 0.006x = 0.2
=> x = 33.33%

Thus, new price = 1+x% of 1 = $1.33

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